Number System
Number system is a fundamental topic in quantitative aptitude that deals with properties of numbers, divisibility rules, factors, multiples, and remainders. It is one of the most important topics for banking, SSC, CMAT, and placement exams.
Fundamental Principles
Natural Numbers
Counting numbers starting from 1 (1, 2, 3, ...).
Whole Numbers
All natural numbers including 0 (0, 1, 2, 3, ...).
Integers
Includes negative numbers, zero, and positive numbers (..., -2, -1, 0, 1, 2, ...).
Prime Numbers
Numbers greater than 1 having exactly two factors: 1 and itself (e.g., 2, 3, 5, 7).
Composite Numbers
Numbers having more than two factors (e.g., 4, 6, 8, 9).
Essential Formulation Tips
- Learn divisibility rules from 2 to 11 for faster solving.
- Memorize squares up to 30 and cubes up to 20.
- Use factorization to simplify large numbers.
- Always check for common factors in problems.
Shortcut Execution Techniques
- Divisibility by 9: Sum of digits should be divisible by 9.
- Divisibility by 11: Difference between sum of alternate digits should be multiple of 11.
- Even numbers are divisible by 2; numbers ending in 0 or 5 are divisible by 5.
- Use last digit concept to find unit digit quickly.
Contextual Inquiries (FAQs)
Q: What is the most important topic in number system for aptitude?
A:
Q: How to solve number system questions quickly?
A:
Example Breakdown: Divisibility Rule Example
Basic divisibility concept.Sum of digits = 7 + 2 + 9 = 18.
18 is divisible by 9.
Therefore, 729 is divisible by 9.
Final Answer: Yes.
Example Breakdown: HCF Example
Most common exam question.Factors of 12 = 1, 2, 3, 4, 6, 12.
Factors of 18 = 1, 2, 3, 6, 9, 18.
Common factors = 1, 2, 3, 6.
Highest = 6.
Final Answer: 6.
Example Breakdown: Unit Digit Example
Important shortcut question.7^2 = 49 → unit digit = 9.
7^4 = (7^2)^2 = 49^2.
Unit digit of 9^2 = 81 → 1.
Final Answer: 1.
Basics Practice Set 1: Natural and Whole Numbers
Fundamental concepts regarding natural numbers, whole numbers, and basic operations.
Q1. Which of the following is a natural number?
Q2. Which number is the smallest whole number?
Q3. What is the sum of the first 3 natural numbers?
Q4. Is 0 a natural number?
Q5. Which set contains only whole numbers?
Q6. What is 10 multiplied by 0?
Q7. Which of these is a counting number?
Q8. The number 15 is a:
Q9. Which is greater: 10 or 100?
Q10. The number 0 is: